## NAND Gate and Logical Networks

### Objective:

To show that the NAND gate is a complete gate and to analyze logical networks

### Introduction:

In the previous experiment, all the basic logic gates were studied. A set of gates necessary to implement every Boolean function is a complete set. AND, OR and INVERTER make a complete set. NAND is also a complete set.

### Procedure:

Show a network of NAND gates to function as:

1. INVERTER
2. 2-input AND
3. 2-input OR

Wire up the circuits and verify their operations.

#### Decimal to Binary Encoder:

To communicate with a computer, it is necessary to convert input information into a binary form that the computer understands. One device that does this translation is an encoder. An encoder is a device that has 2n (or fewer) inputs and n outputs. The outputs generate the binary version of the inputs. Figure 1 shows an encoder for converting the decimal digits 0 to 7 to their binary equivalents. Construct this encoder.

Figure 1 - Binary Encoder using NAND gates

1. Set all switches to 1 Observe and record the condition of the LED's.
2. Reset switch 1 to level (0), observe and record the condition of the LED's.
3. Set switch 1 to level (1) and reset switch 2 to (0), observe and record the conditions of the LED's.
4. Continue setting one switch at a time and record the indication of the LED's. Demonstrate your circuit to the instructor.
5. Explain the operation of the encoder used by explaining the operation of each gate.
6. Design (on paper only) an encoder to convert the decimal numbers 0 to 15 into binary.

#### Decoder:

When a computer has completed an operation, the answer is usually given in binary form that is required to be decoded to decimal form for most people. A decoder could do this function. It has n inputs and 2n outputs. A decoder using NAND gates is shown below. Construct this decoder.

Figure 2 - Decoder using NAND and INVERTER gates

1. Analyze the above circuitry by constructing the truth table. Explain how the logic elements operate.
2. With all switches in 0 position, observe and record the LED outputs.
3. Switch in all possible combinations of the input switches. Observe and record the LED outputs. Compare it with the truth table constructed. Demonstrate your circuit to the instructor.
4. Design (on paper only) the circuitry to decode the binary numbers up to 1111 into decimal.